NEW YORK (Reuters) - Japan has sovereignty over the islands at the heart of a dispute with China and therefore will not compromise on ownership, Prime Minister Yoshihiko Noda said on Wednesday.

"They are an inherent part of our territory in light of history and also under international law," Noda said in reference to the Senkaku Islands.

"Therefore, there cannot be any compromise that represents a retreat from this position," he told a news conference in New York after attending the U.N. General Assembly.

(Reporting By Paul Eckert; Editing by David Brunnstrom)